1. **State the problem:** We have a sample of 20 people watching a commercial. The success rate for recalling the company name is 81% or 0.81. We want to find: a) The expected number of people who recall the company name. b) The probability that 11 or fewer people recall the company name, assuming the success rate is 0.81. 2. **Formula for expected value:** The expected number of successes in a binomial distribution is given by: $$E = n \times p$$ where $n$ is the number of trials (people), and $p$ is the probability of success. 3. **Calculate expected number:** $$E = 20 \times 0.81 = 16.2$$ So, the expected number of people recalling the company name is 16.2. 4. **Probability calculation:** We model the number of people recalling the name as a binomial random variable $X \sim \text{Binomial}(n=20, p=0.81)$. We want to find $P(X \leq 11)$. 5. **Using binomial probability:** The probability is the sum of probabilities from $k=0$ to $k=11$: $$P(X \leq 11) = \sum_{k=0}^{11} \binom{20}{k} (0.81)^k (0.19)^{20-k}$$ 6. **Calculation (using a calculator or software):** This sum evaluates approximately to 0.0002 (rounded to four decimal places: 0.0002). 7. **Interpretation:** The probability of 11 or fewer people recalling the company name, assuming the campaign is successful, is very low (0.0002), indicating that 11 or fewer is unlikely under the success assumption. **Final answers:** - Expected number: 16.2 - Probability $P(X \leq 11) \approx 0.0002$